CCN_600_5 · 612 W · 1100 mm·min⁻¹ · med mesh · η 0.45 · t = 250 ms (run complete)

Tracking the Deepest Point of the Melt Pool

Longitudinal section of the whole simulated track, the full 7.6 mm domain. Dark is the fusion boundary that has already set (this is what a metallographic cut shows); orange is the metal that is fully liquid at this moment (liquid fraction 1). Behind the beam the track falls into three stretches, and their boundaries are marked. The penetration depth fluctuates irregularly along the track and still rises with x: within the 250 ms simulated, the pool is still deepening and lengthening, which is not long enough to observe a steady pool behaviour.

Longitudinal section of the whole domain

Vertical exaggeration —×. Drag the slider to watch the pool advance along the track; the dark fusion record freezes behind it. The blue band is the extent covered by the beam, D4σ = 2.00 mm (r₀ = 707 µm).

The orange region encloses fully liquid metal on the symmetry plane y = 0: T ≥ 1729.1 K, the liquidus of the solver's solidification model. The solver sets the liquid fraction linearly in temperature between the solidus 1661.3 K and the liquidus 1729.1 K (the phase lines of the nominal bead composition f = 0.3232, used for every composition), so the liquid fraction is 1 inside the orange region; the 1661.3–1729.1 K layer just outside it is the mushy zone, with a liquid fraction between 0 and 1. The dark fusion boundary is read from the peak temperature 1771 K (the liquidus of 4140, decision D5), which is a different quantity.

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Mean cross-section of the fully solid stretch, overlaid on the measured metallograph

The simulated outline is the mean of the 40 sections that are fully solid at 250 ms (x = 3.01–3.95 mm): the fusion boundary is the iso-surface peak temperature = 1771 K, and the bead surface is the metal height column by column (at 250 ms the once-molten metal in these sections is still at 949–1613 K, median 1147 K, and the surface still includes the thermal lift of the substrate). The measurement is the etched cross-section of the same condition (0822 curve, SHA256 3e4a2b03fc1d…). Both are aligned with the original substrate surface at z = 0 and the pool centre at y = 0, at the same scale horizontally and vertically.

QuantitySimulationMeasuredDifferenceSimulation basis

What one cross-section goes through after the beam centre passes

Follow one fixed cross-section of the track and start the clock when the beam centre is over it; distances convert to time with the scan speed 18.333 mm/s. The beam is 2.00 mm wide by D4σ, and its trailing edge (1.00 mm behind the centre) leaves the section only at +54.5 ms.

0 – 42 ms

Still under the beam; the fusion boundary grows outwards

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The beam centre has passed, but the section is still under the rear half of the beam (it leaves the beam only at +54.5 ms) and keeps being heated; the melting front advances downwards and sideways. The fusion boundary read from the peak temperature 1771 K reaches its final position about 42 ms after the beam centre has passed (decision D27).

from 42 ms

Boundary set; the liquid shrinks

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The fusion boundary no longer moves outwards; this is the outline a metallographic cut shows. The section still holds liquid metal, but the liquid only shrinks; until it solidifies, the section still receives CCN carried back by the flow from the pool ahead.

from 115.2 ms

Solidification complete

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All liquid has gone. In the 250 ms snapshot the tail of the liquid trails the beam centre by 2.11 mm; this interval grows as the pool lengthens: 104 ms at 200 ms, 111 ms at 225 ms, 115.2 ms at 250 ms.

The set stretch against the measurement

The 96 set sections at x = 3.01–5.29 mm at 250 ms (the beam centre passed them more than 42 ms earlier, so their fusion geometry no longer changes). Their penetration depth fluctuates from section to section and still rises along x, so the table gives the mean and the range, not a steady value.

QuantitySimulation meanSimulation rangeMeasuredDifference of means
Depth D / µm144.1121.3 – 165.4181.5-20.6%
Width W / µm11121074 – 1135974.2+14.2%
Aspect ratio D/W0.12950.1863-30.5%
Fusion area / µm²108 997117 175-7.0%

Bead area: compared by mass

The simulated bead is compared with the measured bead area 55 958 µm² through the CoCrNi mass per unit track length ÷ 7900 kg/m³.

  1. This density has the same origin as the powder feed rate. The simulated feed rate was back-calculated from the measured bead area: ṁ = Ameasured × v × ρdep, ρdep = 7900 kg/m³, and the case journal has ded/mdot = 8.1045e-06 kg/s. The CoCrNi fed per unit track length therefore converts, at the same density, to 55 958 µm², exactly the measured bead area.
  2. The CoCrNi mass in the simulation is book-kept by the conserved f field. The last monitor line (t = 250.0 ms): CoCrNi in the f field 1.9542e-06 kg, cumulative powder source 1.9363e-06 kg, ratio 1.009. Integrating the section table over x gives 1.9542e-06 kg, in agreement.
  3. This quantity does not change with temperature. It is a mass and does not shrink as the section cools, unlike the metal area at z > 0; it holds both for sections still hot at 250 ms and for the metallographic section at room temperature.

The 40 fully solid sections at 250 ms (x = 3.01–3.95 mm): the mean bead area converted from mass is 67 771 µm² (65 090 – 70 107), 116%–125% of the measurement (mean +21.1%). The excess comes from the pool still lengthening: between 225 and 250 ms the tail of the liquid advances at only 15.4 mm/s, slower than the beam's 18.333 mm/s, so each solidified stretch of track receives more CoCrNi than feed rate ÷ scan speed. Once the pool stops lengthening, the two should be equal.

The metal area at z > 0, Σα, cannot be used for the comparison. Over the same sections its mean is 99 811 µm², and it contains two terms unrelated to deposition: first, the substrate expands when heated and its surface lifts — sections at x < 0.6 mm (never molten, never reached by powder) also show 11 814 and 12 237 µm² at 225 ms and 250 ms; second, the section keeps cooling and contracting after solidification, and this area shrinks with it (see the "Melt Pool Mixing Timeline" page).

Penetration depth along the track (250 ms)

Over the set stretch x = 3.01–5.29 mm the depth rises at +7.1 µm/mm (dashed line: linear fit); the standard deviation of the sections about the fit is 9.1 µm. The grey band is the stretch not yet set. The red dashed line is the measured 181.5 µm.

How far the deepest point trails the beam

The deepest point of the fully liquid region (metal at T ≥ 1729.1 K on the symmetry plane) is always behind the beam centre: 0.22 mm at 25 ms, 0.72 mm at 250 ms (0.22–0.82 mm over 25–250 ms).

How to read it

42 ms
About 42 ms after the beam centre has passed, the depth reading of a section stops changing. x = 2.988 mm (passed by the beam 169 ms before t = 250 ms) reads, in the 8 snapshots over 162.5–250 ms, 121.1, 121.1, 121.1, 121.1, 121.1, 121.1, 121.1, 121.1 µm; x = 3.300 mm (passed 152 ms before t = 250 ms) reads 128.2, 128.2, 128.2, 128.2, 128.2, 128.2, 128.2, 128.2 µm in the same 8 snapshots. x = 4.596 mm (passed 81 ms before t = 250 ms) reads 57.0, 110.3, 140.5, 153.1, 153.5, 153.5, 153.5, 153.5 µm in the same 8 snapshots: the reading grows while less than 42 ms have passed since the beam centre, and stays constant afterwards.
Fluctuation
The depth fluctuates irregularly along the track; no steady pattern shows within 250 ms. Over the set stretch the depth is 121.3–165.4 µm, deepest 165.4 µm (x = 4.524 mm); after removing the linear trend, the spacing between neighbouring extrema ranges over 0.024–0.576 mm, a factor of 24, with no discernible period (consistent with the conclusion of the closed screening of the sources of the depth fluctuation). The depth also still rises with x: the first half of the set stretch averages 140.1 µm, the second half 148.0 µm. At 250 ms the set track covers only 3.01–5.29 mm while the pool is still deepening and lengthening; this simulated time is not long enough to judge whether the pool reaches a steady state or whether the fluctuation has a pattern. That needs a longer simulation, until the depth no longer rises with x.
Solidification
At 250 ms the sections containing liquid (liquid fraction > 0) form one stretch of 2.57 mm (x = 3.972–6.540 mm, 108 sections); its front is 0.46 mm ahead of the beam centre, and its tail 2.11 mm behind it, i.e. 115.2 ms. A section therefore sets about 42 ms after the beam centre has passed and is fully solid after about 115.2 ms.
Bead
The bead is compared with the measurement by mass (section "Bead area: compared by mass" above). On the centreline the metal height at z > 0 is 66.9–91.1 µm over the fully solid stretch (mean 81.0), against a measured bead height of 98.4 µm; the former is read while still hot at 250 ms and includes the thermal lift of the substrate (about 2.0 µm far from the track), so it serves only as a reference.